Caulking Fiberglass Shower Stall

We installed a small (36") three-piece fiberglass shower stall about 25 years ago. The unit has a base and two wall pieces that join at in the middle of the back wall. We use it daily and plan to replace it with something nice some time down the road, but it isn't in the budget right now.
The problem is the caulk in the joints regularly become moldy. All the regular methods of cleaning only lasts a short time and the mold returns. I think my best attack would be to remove and replace the old dried out caulk. Problem is how to get the old hard caulk out without major damage to the fiberglass. The joints are pretty small, 1/8 inch or less, so there is not much work room.
Before I go at it with my utility knife, I thought I'd see if anyone had any better ideas.
Thanks!
Mark
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It is the kind of caulk that remains flexible when it dries?
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I'm pretty sure I used a fairly good grade when I first installed the stall - it's lasted this long, but it is pretty hard at now.

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I asked because my idea could either be a great one if the caulk's hard, or a real bust if it's soft. I'd use a variable speed Dremel with a very skinny bit, like this grout removal bit: http://www.dremel.com/en-us/attachments-and-accessories/attachment-accessory-detail.htm?H8549&Gf357&If362
If you held it very steady, you should be able to grind out the caulk. But, if the caulk's soft, it might want to grab the bit and make tool stall. Safety goggles are obviously a necessity. If this idea worked, it would be a great excuse for buying another tool.

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I
caulk.
not
any
Something softer than the fiberglas, but harder than the caulk. Look in the kitchen utensil aisle for those plastic doohickeys used to skin fruit. Or put a point on some old toothbrush handles. Some of the plastic tools used for working Bondo may be useful. Once you get an end started, grab it with pliers and pull. A little alchohol and a kitchen scrubber may be useful to clean up residue.
aem sends...
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And once you get the old stuff off re-caulk it with 100% silicone.
I used tub & tile caulk - the latex type & had the same problem. Replaced it with silicone & it has looked good for years.
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